scholarly journals A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 693 ◽  
Author(s):  
Abubakar ◽  
Kumam ◽  
Awwal ◽  
Thounthong
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Signal Reconstruction ◽  
Gradient Algorithm ◽  
Sparse Signal ◽  
Signal Recovery ◽  
Numerical Examples ◽  
Monotone Equations ◽  
Nonlinear Monotone Equations ◽  
Self Adaptive

In this article, we propose a modified self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established. Numerical examples reported show that the method is promising and efficient for solving monotone nonlinear equations. In addition, we applied the proposed algorithm to solve sparse signal reconstruction problems.

scholarly journals An Accelerated Conjugate Gradient Algorithm for Solving Nonlinear Monotone Equations and Image Restoration Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Haishan Feng ◽  
Tingting Li
Keyword(s):  
Image Restoration ◽  
Conjugate Gradient ◽  
Trust Region ◽  
Step Length ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Search Technique ◽  
Conjugate Gradient Algorithms ◽  
Monotone Equations ◽  
Nonlinear Monotone Equations

Combining the three-term conjugate gradient method of Yuan and Zhang and the acceleration step length of Andrei with the hyperplane projection method of Solodov and Svaiter, we propose an accelerated conjugate gradient algorithm for solving nonlinear monotone equations in this paper. The presented algorithm has the following properties: (i) All search directions generated by the algorithm satisfy the sufficient descent and trust region properties independent of the line search technique. (ii) A derivative-free search technique is proposed along the direction to obtain the step length αk. (iii) If ϕk=−αkhk−hwkTdk>0, then an acceleration scheme is used to modify the step length in a multiplicative manner and create a point. (iv) If the point satisfies the given condition, then it is the next point; otherwise, the hyperplane projection technique is used to obtain the next point. (v) The global convergence of the proposed algorithm is established under some suitable conditions. Numerical comparisons with other conjugate gradient algorithms show that the accelerated computing scheme is more competitive. In addition, the presented algorithm can also be applied to image restoration.

scholarly journals A modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations

2021 ◽  
Author(s):  
Mompati Koorapetse ◽  
P Kaelo ◽  
S Kooepile-Reikeletseng
Keyword(s):  
Global Convergence ◽  
Projection Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Numerical Results ◽  
Projection Technique ◽  
Monotone Equations ◽  
Derivative Free ◽  
Nonlinear Monotone Equations

In this paper, a new modified Perry-type derivative-free projection method for solving large-scale nonlinear monotone equations is presented. The method is developed by combining a modified Perry's conjugate gradient method with the hyperplane projection technique. Global convergence and numerical results of the proposed method are established. Preliminary numerical results show that the proposed method is promising and efficient compared to some existing methods in the literature.

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